Question

a.  When a fair die is thrown, numbers 1 through 6 would appear with equal probability of 1/6. The mean is 3.5 and variance is 2.92.

If 57 dice are thrown, what is the variance of their sum?

b .

When a fair die is thrown, numbers 1 through 6 would appear with equal probability of 1/6. The mean is 3.5 and variance is 2.92.

If 40 dice are thrown, what is the mean of their sum?

c.

Let X be a Normal random variable with mean 30 and standard deviation 8.  Find its 60th percentile (i.e. find a number y such that P(X < y) = 0.6)

(provide one digit to the right of decimal point)

d.

Let X be a Normal random variable with mean 30 and standard deviation 8.  Find P(32 < X < 40).   (provide four digits to the right of the decimal point)

Answer 1